Hello group,
I do have some problems with MATLAB algorithms for controller synthesis (H-infinity with Ricatti/LMI solver). I'm not sure what is the reason for it, so I'm trying to figure it out. There are two things that I could think of: the model is to stiff, so the algorithm have numerical problems, or I do have a problem with a algebraic loop.
The nonlinear Simulink model contained a algebraic loop, so a PT1 function with a fast pole (tf([1000],[1 1000])) was added to avoid the algebraic loop and get the model work. There also exist linear state space models of the subsystems. When I connect the state space models of the subsystems in Simulink (this was first done for better validation in Simulink, later with append/connect), I get a warning that there exist a algebraic loop, but the simulation works and the results (outputs) are realistic.
But when I append+connect the various state spaces to one big state space model and simulate it, there aren't any warnings. What happens to the algebraic loop? Does it still exist within the state space? How does Matlab handle theses algebraic calculations or are they in any way ignored?
The other problem might be the stiffness of my model. I have a stable system, but the left poles are at about -10^3 and the right poles are near the imaginary axis at about -10^-4.
Could it be the algebraic loop that makes the model stiffer?
All algorithms that I use have problems my model. It is of order >40. If I use the Ricatti algorithms with a reduced order model (balanced realization) it works, but the results aren't very good, when I simulate the controller in the original full order model. So I need to make the controller design with the full order model in order to account all dynamics.
What do you think? Any suggestions or hints? If you need further information, please tell me. Greetings, Clemens